Measuring the effect of different political actions to contrast the contagion of COVID19
Angela Andreella, Michele Lambardi, Silvia De Nicolò
03th June, 2020
1 Introduction
Since the beginning of the COVID-19 epidemic, policy makers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures and stay-at-home recommendations and including in addition the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.
The timing of the different interventions with respect to the spread of the contagion both at a global and intra-national level has been very different from country to country. This, in combination with demographical, economic, health-care related and area-specific factors, have resulted in different contagion patterns across the world.
Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.
Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.
In doing so, some issue arises concerning the identification and codification of the different measures undertaken by governments, the analysis related to whether a strategies resemblance can be detected across countries and the measurement of the effects of containment policies on contagion. Thus, after an introductory section explaining data and variables, a second section regards some explanatory analysis facing the codification of containment policies and the strategies resembling patterns. The third section deals with the measurement of policies effect from a global perspective, lastly the forth section analyze Italian lockdown and regional outcomes. Conclusion are drawn in the last section.
2 Data and Variables
The data repositories used for this project are COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University1 for contagion data (Dong, Du, and Gardner (2020)), and Oxford COVID-19 Government Response Tracker (OxCGRT)2 for policies tracking (Thomas et al. (2020)), together with World Bank Open Data Repository for demographic data.
Contagion data..
The Oxford COVID-19 Government Response Tracker (OxCGRT) collects all the containment policies adopted by government worldwide by making available information on 11 indicators of government containment responses of ordinal type. These indicators measure policies on a simple scale of severity / intensity and are reported for each day a policy is in place, specifying if they are “targeted”, applying only to a sub-region of a jurisdiction, or a specific sector; or “general”, applying throughout that jurisdiction or across the economy.
The containment ordinal variables considered are:
School closing records closings of schools and universities with levels: 0 - No measures 1 - recommend closing 2 - Require closing (only some levels or categories, eg just high school, or just public schools) 3 - Require closing all levels.
Workplace closing records closings of workplaces with levels:0 - No measures 1 - recommend closing (or work from home) 2 - require closing (or work from home) for some sectors or categories of workers 3 - require closing (or work from home) all-but-essential workplaces (e.g. grocery stores, doctors).
Cancel public events records cancelling public events with levels: 0- No measures 1 - Recommend cancelling 2 - Require cancelling.
Restrictions on gatherings records the cut-off size for bans on private gatherings with levels: 0 - No restrictions 1 - Restrictions on very large gatherings (the limit is above 1000 people) 2 - Restrictions on gatherings between 101-1000 people 3 - Restrictions on gatherings between 11-100 people 4 - Restrictions on gatherings of 10 people or less.
Close public transport records closing of public transport with levels: 0 - No measures 1 - Recommend closing (or significantly reduce volume/route/means of transport available) 2 - Require closing (or prohibit most citizens from using it).
Stay at home requirements records orders to “shelter-in- place” and otherwise confine to home with levels: 0 - No measures 1 - recommend not leaving house 2 - require not leaving house with exceptions for daily exercise, grocery shopping, and ‘essential’ trips 3 - Require not leaving house with minimal exceptions (e.g. allowed to leave only once a week, or only one person can leave at a time, etc.).
Restrictions on internal movement records restrictions on internal movement with levels: 0 - No measures 1 - Recommend not to travel between regions/cities 2 – internal movement restrictions in place.
International travel controls records restrictions on international travel with levels: 0 - No measures 1 - Screening 2 - Quarantine arrivals from high-risk regions 3 - Ban on arrivals from some regions 4 – Ban on all regions or total border closure.
Public info campaigns records presence of public info campaigns with levels: 0 -No COVID-19 public information campaign 1 - public officials urging caution about COVID-19 2 - coordinated public information campaign (e.g. across traditional and social media).
Testing policy describing who can get tested by public health system with levels: 0 – No testing policy 1 – Only those who both (a) have symptoms AND (b) meet specific criteria (e.g. key workers, admitted to hospital, came into contact with a known case, returned from overseas) 2 – testing of anyone showing COVID-19 symptoms 3 – open public testing (e.g. “drive through” testing available to asymptomatic people).
3 Containment strategies and resembling patterns
Identification and codification of different measures undertaken by governments performed by University of Oxford results in 11 ordinal variables selected as lockdown policies. This sets up the necessity to analyze and to aggregate them in a synthetic way in order to find out whether specific combinations of those policies making up political strategies come out to have a resemblance pattern across countries.
Therefore, we performed a Principal Component Analysis based on the polychoric correlation. It allows to estimate the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. It has no closed form but it is estimated via MLE assuming the two latent variables follows a bivariate normal density.
The interpretation of the first three principal components (accounting for the 80% of total variance) appears to be clear (see Figure ): the first one is closely related with freedom of movements and gathering restrictions together with information campaigns strategy, crucial in cases of draconian measures, the second one is related with the strategy of informing and testing the population, lastly the third one is related to informing and contact tracing the population. Summarizing, on one hand a first containment strategy aims at social distancing the entire population, on the other hand a second one aims at act locally and rapidly detect and isolate the positive cases, with two (alternative or complementary) tools: tracing contacts of infected and/or blanket population testing.
First 3 Principal Components Loadings.
We want now to figure out which countries have adopted the undelined strategies and whether there is a strategies resemblance across countries, considering both the combination of measures undetaken and the timing w.r.t. the day of the first contagion detection on country soil. In order to do so, we performed a functional co-clustering of the first three principal components taking into account 20 countries in a specific time span (which varies from country to country) that depends on when the first covid cases has been detected on national soil. We perfomed an alignment of the contagion pattern from the 10th day before first contagion detection, in order to include also relevant information on the prevention measures.
Considering a matrix of 20 countries (rows) of 3 curves (columns or functional features- restriction-based, testing-based and tracing-based policies) s.t. \(x=(x_{ij}(t))_{1\leq i \leq 20; 1 \leq j\leq3}\) with \(t \in [0,85]\), we reconstructed the functional form of the data from their discrete observations (85 days) by assuming that curves belong to a finite dimensional space spanned by a basis of functions and then we estimated a functional latent block model used for co-clustering.
The two policies clusters depicts Restriction-based policies on one hand, Tracing and Testing-based policies on the other hand, confirming that these last two policies reflects a common strategy as described above.
The countries clusters are displayed in Figure : (South Korea, Singapore), (Germany, Sweden), (USA, Canada, Greece, Portugal), (Italy, Spain, Ireland, UK, Netherlands), (Norway, Denmark, Finland, France, Belgium, Switzerland, Austria). The interpretation can be grasped in Figure . South Korea and Singapore political strategy is characterized by the detection and isolation of the positive cases via contact tracing and mild testing policies, without any relevant social distancing action. On the contrary Germany, Sweden strategy was to detect and isolate positive cases via an extensive testing policy strategy, without any strong social distancing measures in order to protect the economy. A very different strategy has been adopted by the cluster including Italy, Spain, Ireland, UK and Netherlands, which acted with social distancing measures at different temporal stages (considering in particular the north european countries of the cluster) but promptly with respect to the first contagion inside national borders. In particular the strategies of Ireland, UK and Netherland was very strict concerning school and workplace closing as well as gathering and international movement restiction, weaker as regards stay at home recommendations, internal movement restriction and transport closing but at the same time relying on a strong information campaign. On the other hand, Italy and Spain sharpened up stay at home and internal movement restrictions. USA, Canada, Greece and Portugal has adopted intermittently social distancing measures in addition with strong social tracing during the second part of the considered period. Lastly, Norway, Denmark, Finland, France, Belgium, Switzerland, Austria has adopted intermediate social distancing measure, in line with other European countries, but without any relevant testing or tracing measure in addition.
Clusters map.
Clusters average functionals related to Social Distancing Restrinction, Testing and Tracing policies aligned at the day of the first contagion (vertical blue line).
4 Effect of policies from a global perspective
Some countries have underestimated the dangerousness of the Coronavirus disease 2019 (COVID-19) and the importance to apply the containment measures. The little concern of some countries regarding the COVID-19 infectious disease is due by many and different reason. Some countries decided to save the economy instead of people lives, i.e., it is a method to fight a war, in this case the pandemic war. For that, we want to analyze which coutries adopt the ``optimal’’ policy measures to contain the contagion of COVID-19. Thanks to the Thomas et al. (2020) data sets, we know which type of measures each goverment take and when. The indicators of government response considered are \(17\) in total, that can be resumed in indicators of lockdown/social distancing, contact tracing, movement restrictions, testing policy, public health measures, and governance and socio-economic measures.
Therefore, some variables as the number of hospital beds are considered from OECD in order to have some additional covariates that can be influence the variation in government responses to COVID-19.
We restrict the wide range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.
The daily number of active person is analyzed as measure of COVID-19 situation. Being a count variable, we decide to use a Negative Binomial Regression in order to correct also for the possible overdispersion. Therefore, the hierarchical struture induced by the nested structure of countries inside the clusters and by the repeated measures statement. For that, we think to use a generalized mixed model with family negative binomial. The countries information as well as the clusters and date information are used as random effects in our model.
So, the aim is to understand how the lockdown policies influences the contagions. We consider the aligned data respect to the first confirmed case, we have the following situation:
Also, we lag the number of active respect to \(14\) days, in order to consider the influences of the restrictions imposed at time \(t\) on number of active at time \(t+14\), in order to make a correct impact. The observations are aligned respect to the first confirmed case across the countries, in order to have observations directly comparable in a longitudinal point of view.
4.1 Exploratory Analysis
The set of covariates considered in this analysis can be divided into three main area:
Longitudinal economic variables;
Longitudinal health vystem variables;
Fixed demographic/economic/health variables.
4.1.1 Economic Variables
| Name | Measurement | Description |
|---|---|---|
| Income Support | Ordinal | Government income support to people that lose their jobs |
| Debt/contract relief for households | Ordinal | Government policies imposed to freeze financial obligations |
| Fiscal measures | USD | Economic fiscal stimuli |
| International support | USD | monetary value spending to other countries |
We will combine these two first economic variables into one continous variables using the Polychoric Principal Component Analysis, in order to diminuish the number of covariates inside the model, having \(9\) ordinal policies lockdown covariates.
FALSE Converted non-numeric input to numericTherefore, the two economic variables in USD are examined and transformed in logarithmic scale in order to de-emphasizes very large values.
For further details about the definition of the economic variables, please see
4.1.2 Demographic/Fixed variables
4.1.3 Health variables
| Name | Measurement | Description |
|---|---|---|
| Emergency Investment in healthcare | USD | Short-term spending on, e.g, hospitals, masks, etc |
| Investment in vaccines | USD | Announced public |
| spending on vaccine development |
FALSE Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.FALSE `geom_smooth()` using method = 'loess' and formula 'y ~ x'FALSE Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.FALSE `geom_smooth()` using method = 'loess' and formula 'y ~ x'pca.
4.2 Model
The data are observed for each country nested within date.
Two-level model: the units of analysis (Level 1), countries, are nested within clusters (Level 2), date;
The variability of the data comes from nested sources;
The Intraclass Correlation Coefficient (ICC) is equal to \(0.3910876\) for date, equals \(0.04668614\) for id and $ 0.02533497$ for Clusters.
lot to understand the variability respect date
and respect Clusters:
and id:
How to choose the random and fixed part?
The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices.
-Conditional AIC (Package cAIC4): The conditional AIC is also appropriate for choosing between a simple null model without any random effects and a complex model incorporating random effects,
-Boostrap (R Package pbkrtest): Model comparison of nested models using parametric bootstrap methods. Implemented for some commonly applied model types.
Finally the model is:
FALSE Family: nbinom2 ( log )
FALSE Formula:
FALSE active_lag ~ pca_EC + pop_density_log + surface_area_log + pca_hs +
FALSE workplace_closingF + gatherings_restrictionsF + transport_closingF +
FALSE stay_home_restrictionsF + testing_policyF + contact_tracingF +
FALSE Clusters + (0 + pca_LD | id) + (1 | date2) + (1 | Clusters)
FALSE Data: dat
FALSE Offset: log(active + 1)
FALSE
FALSE AIC BIC logLik deviance df.resid
FALSE 40748.6 40921.6 -20344.3 40688.6 2330
FALSE
FALSE Random effects:
FALSE
FALSE Conditional model:
FALSE Groups Name Variance Std.Dev.
FALSE id pca_LD 2.928e-01 5.411e-01
FALSE date2 (Intercept) 4.169e+00 2.042e+00
FALSE Clusters (Intercept) 4.215e-09 6.492e-05
FALSE Number of obs: 2360, groups: id, 20; date2, 158; Clusters, 5
FALSE
FALSE Overdispersion parameter for nbinom2 family (): 1.07
FALSE
FALSE Conditional model:
FALSE Estimate Std. Error z value Pr(>|z|)
FALSE (Intercept) -0.95466 0.70894 -1.347 0.17811
FALSE pca_EC -0.53735 0.07044 -7.629 2.37e-14 ***
FALSE pop_density_log 0.15443 0.04620 3.342 0.00083 ***
FALSE surface_area_log 0.05360 0.03587 1.494 0.13510
FALSE pca_hs 0.05193 0.02029 2.559 0.01050 *
FALSE workplace_closingF1 -0.24604 0.14061 -1.750 0.08016 .
FALSE workplace_closingF2 -1.12441 0.14061 -7.997 1.28e-15 ***
FALSE workplace_closingF3 -0.46986 0.17228 -2.727 0.00638 **
FALSE gatherings_restrictionsF1 -0.52789 0.16317 -3.235 0.00122 **
FALSE gatherings_restrictionsF2 -1.22558 0.14231 -8.612 < 2e-16 ***
FALSE gatherings_restrictionsF3 -1.48631 0.17392 -8.546 < 2e-16 ***
FALSE gatherings_restrictionsF4 -1.67393 0.17987 -9.306 < 2e-16 ***
FALSE transport_closingF1 -0.04257 0.10635 -0.400 0.68897
FALSE transport_closingF2 -0.44643 0.20266 -2.203 0.02761 *
FALSE stay_home_restrictionsF1 -0.06059 0.10879 -0.557 0.57758
FALSE stay_home_restrictionsF2 -0.13755 0.14964 -0.919 0.35799
FALSE stay_home_restrictionsF3 -0.87098 0.29387 -2.964 0.00304 **
FALSE testing_policyF1 0.20317 0.09147 2.221 0.02633 *
FALSE testing_policyF2 0.55401 0.11289 4.908 9.21e-07 ***
FALSE testing_policyF3 1.30708 0.16002 8.168 3.13e-16 ***
FALSE contact_tracingF1 0.20257 0.08292 2.443 0.01456 *
FALSE contact_tracingF2 0.37629 0.09576 3.929 8.51e-05 ***
FALSE ClustersCl2 1.47291 0.17353 8.488 < 2e-16 ***
FALSE ClustersCl3 1.93534 0.15847 12.213 < 2e-16 ***
FALSE ClustersCl4 2.34541 0.14849 15.795 < 2e-16 ***
FALSE ClustersCl5 2.43211 0.16041 15.162 < 2e-16 ***
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE No summary function supplied, defaulting to `mean_se()
5 Italian lockdown and regional outcomes
6 Effect of policies from a global perspective
7 Supplementary materials
All the codes used for this analysis is available on Github.
Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.
Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.